What is the limit as x approaches-0 of f(x)(|x|)/x ?

The limit as x approaches-0 of f(x)(|x|)/x is 0

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limit as x approaches-0 of f(x)(|x|)/x

x \to - 0 lim (f (x) \frac{∣ x ∣}{x})

0

Solution steps

x \to - 0 lim (f (x) \frac{∣ x ∣}{x})

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to - 0 - lim (f (x) \frac{∣ x ∣}{x}) = 0

x \to - 0 + lim (f (x) \frac{∣ x ∣}{x}) = 0

= 0

x \to 2 lim ((5 - 2 x)^{2})

x \to 2 lim (h (x) (2 x - 2))

x \to 1 lim (f (x) g (x))

x \to 3 lim (\frac{3}{x ^{2} - 9})

x \to 5 lim (\frac{x - 5}{x - 25})

What is the limit as x approaches-0 of f(x)(|x|)/x ?
The limit as x approaches-0 of f(x)(|x|)/x is 0